Concept explainers
Interpretation:
3s, 3p and 3d orbitals which have the same energy in a hydrogen atom but different energies in a many-electron atom should be explained by using the concept of quantum numbers and Aufbau principle.
Concept Introduction:
Energies of orbitals in the hydrogen atom
The energies of orbitals in the hydrogen atom depend only on the value of the principal quantum number (n). When n increases, energy also increases. For this reason, orbitals in the same shell have the same energy in spite of their subshell. The increasing order of energy of hydrogen orbitals is
1s < 2s = 2p < 3s = 3p = 3d < 4s = 4p = 4d = 4f
In the case of one 2s and three 2p orbitals in the second shell, they have the same energy. In the third shell, all nine orbitals (one 3s, three 3p and five 3d) have the same energy. All sixteen orbitals (one 4s, three 4p, five 4d and seven 4f) in the fourth shell have the same energy.
The energy levels of the different orbitals in hydrogen atom are easily explained by considering the given diagram. Here, each box represents one orbital. Orbitals with the same principal quantum number (n) have the same energy.
Energies of orbitals in a many electron atom
Energy of an orbital in a many electron atom depends on both the values of principle quantum number (n) and
Principal Quantum Number (n)
The principal quantum number (n) assigns the size of the orbital and specifies the energy of an electron. If the value of n is larger, then the average distance of an electron in the orbital from the nucleus will be greater. Therefore the size of the orbital is large. The principal quantum numbers have the integral values of 1, 2, 3 and so forth and it corresponds to the quantum number in
Angular Momentum Quantum Number (l)
The angular momentum quantum number (l) explains the shape of the atomic orbital. The values of l are integers which depend on the value of the principal quantum number, n. For a given value of n, the possible values of l range are from 0 to n − 1. If n = 1, there is only one possible value of l (l=0). If n = 2, there are two values of l: 0 and 1. If n = 3, there are three values of l: 0, 1, and 2. The value of l is selected by the letters s, p, d, and f. If l = 0, we have an s orbital; if l = 1, we have a p orbital; if l = 2, we have a d orbital and finally if l = 3, we have a f orbital. A collection of orbitals with the same value of n is called a shell. One or more orbitals with the same n and l values are referred to a subshell (sublevel). The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f).
Aufbau principle
In the ground state of an atom, an electron enters the orbital with lowest energy first and subsequent electrons are fed in the order of increasing energies. This is called Aufbau principle. The word 'aufbau' in German means 'building up'. Here, it refers to the filling up of orbitals with electrons. Aufbau principle explains the theoretical, sequential building up of the stepwise addition of protons and electrons for the elements in the periodic table.
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Chemistry: Atoms First
- For the following pairs of orbitals, indicate which is lower in energy in a many-electron atom. (a) 3d or 4s (b) 4f or 3d (c) 2s or 2P d) 4f or 4darrow_forward• identify an orbital (as 1s, 3p, etc.) from its quantum numbers, or vice versa.arrow_forward• list the number of orbitals of each type (1s, 3p, etc) in an atom.arrow_forward
- Which of the following sets of quantum numbers correctly represents a 4p orbital? (a) n = 4, = 0, m = 1 (b) n = 4, = 1, m = 0 (c) n = 4, = 2, m = 1 (d) n = 4, = 1, m =2arrow_forwardSuppose that the spin quantum number did not exist, and therefore only one electron could occupy each orbital of a many-electron atom. Give the atomic numbers of the first three noble-gas atoms in this case.arrow_forwardExplain the difference between (a) the Bohr model of the atom and the quantum mechanical model. (b) wavelength and frequency. (c) the geometries of the three different p orbitals.arrow_forward
- What is the maximum number of electrons that can occupy a f subshell (l = 3)?arrow_forwardWhat type of electron orbital (i.e., s, p, d, or f) is designated by an electron with quantum numbers (a) n=1,l=0,m l =0(b) n=3,l=2,m l =1? (c) n=4,l=3,m l =3arrow_forwardFor the following pairs of orbitals, indicate which is higher in energy in a many-electron atom. (a) 3s or 2P (b) 4s or 4d (c) 4f or 6s (d) 1s or 2sarrow_forward
- Investigating Energy Levels Consider the hypothetical atom X that has one electron like the H atom but has different energy levels. The energies of an electron in an X atom are described by the equation E=RHn3 where RH is the same as for hydrogen (2.179 1018 J). Answer the following questions, without calculating energy values. a How would the ground-state energy levels of X and H compare? b Would the energy of an electron in the n = 2 level of H be higher or lower than that of an electron in the n = 2 level of X? Explain your answer. c How do the spacings of the energy levels of X and H compare? d Which would involve the emission of a higher frequency of light, the transition of an electron in an H atom from the n = 5 to the n = 3 level or a similar transition in an X atom? e Which atom, X or H, would require more energy to completely remove its electron? f A photon corresponding to a particular frequency of blue light produces a transition from the n = 2 to the n = 5 level of a hydrogen atom. Could this photon produce the same transition (n = 12 to n = 5) in an atom of X? Explain.arrow_forwardWhat experimental evidence supports the quantum theory of light? Explain the wave-particle duality of all matter .. For what size particles must one consider both the wave and the particle properties?arrow_forward
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